Studies of a scheme for low emittance muon beam production from positrons on target

A new scheme to produce muon beams characterised by very low emittance, in such a way to avoid the need for cooling, using a positron beam of about 45 GeV interacting on electrons on target is being studied by our group. This scheme is challenging and innovative, and needs a full design study to be developed. In particular, one of the novel topics to be investigated is the interaction between the positron beam stored in a low emittance ring with a thin target, to be inserted directly in the ring chamber to produce muons.Produced muons will then be immediately collected at the exit of the target and transported to two $\mu^+$ and $\mu^-$ accumulator rings. In this paper, after having highlighted the rational in designing a muon collider, we descrive in detail this new muon production scheme, discussing the simulation of the e+ beam interacting with the target, its degradation in the 6-D phase space and the optimisation of the e+ ring design mainly to maximise the energy acceptance.